Problem: Simplify the expression. $(5a+1)(-4a+8)$
First distribute the ${5a+1}$ onto the ${-4a}$ and ${8}$ $ = {-4a}({5a+1}) + {8}({5a+1})$ Then distribute the ${-4a}.$ $ = ({-4a} \times {5a}) + ({-4a} \times {1}) + {8}({5a+1})$ $ = -20a^{2} - 4a + {8}({5a+1})$ Then distribute the ${8}$ $ = -20a^{2} - 4a + ({8} \times {5a}) + ({8} \times {1})$ $ = -20a^{2} - 4a + 40a + 8$ Finally, combine the $x$ terms. $ = -20a^{2} + 36a + 8$